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This paper considers the objectives of accurate stereo matching, especially at object boundaries, robustness against recording or illumination changes and efficiency of the calculation. These objectives lead to the proposedSemi-Global Matching method that performs pixelwise matching based on Mutual Information and the approximation of a global smoothness constraint. Occlusions are detected and disparities determined with sub-pixel accuracy. Additionally, an extension for multi-baseline stereo images is presented. There are two novel contributions. Firstly, a hierarchical calculation of Mutual Information based matching is shown, which is almost as fast as intensity based matching. Secondly, an approximation of a global cost calculation is proposed that can be performed in a time that is linear to the number of pixels and disparities. The implementation requires just 1 second on typical images.